If I purchased a domain name from namecheap.com but want to host the website on it at Host Gator, can I?

Basically, I purchased a domain name from namecheap.com then registered to host it on hostgator.com. It had me enter the domain that I owned and the registration went through fine. I installed Wordpress to the domain through Host Gator's interface but now it says that page doesn't exist. Do I have to register the domain through the company that I host it at? Or did I just do something wrong?